{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial regression with linear models and neural network\n",
    "* Are Linear models sufficient for handling processes with transcedental functions?\n",
    "* Do neural networks perform better in those cases?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Global variables for the program"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N_points = 500 # Number of points for constructing function\n",
    "x_min = 1 # Min of the range of x (feature)\n",
    "x_max = 10 # Max of the range of x (feature)\n",
    "noise_mean = 0 # Mean of the Gaussian noise adder\n",
    "noise_sd = 2 # Std.Dev of the Gaussian noise adder\n",
    "ridge_alpha = tuple([10**(x) for x in range(-3,0,1) ]) # Alpha (regularization strength) of ridge regression\n",
    "lasso_eps = 0.001\n",
    "lasso_nalpha=20\n",
    "lasso_iter=1000\n",
    "degree_min = 2\n",
    "degree_max = 8"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generate feature and output vector following a non-linear function\n",
    "$$ The\\ ground\\ truth\\ or\\ originating\\ function\\ is\\ as\\ follows:\\  $$\n",
    "\n",
    "$$ y=f(x)= x^2.sin(x).e^{-0.1x}+\\psi(x) $$\n",
    "\n",
    "$$: \\psi(x) = {\\displaystyle f(x\\;|\\;\\mu ,\\sigma ^{2})={\\frac {1}{\\sqrt {2\\pi \\sigma ^{2}}}}\\;e^{-{\\frac {(x-\\mu )^{2}}{2\\sigma ^{2}}}}} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x_smooth = np.array(np.linspace(x_min,x_max,501))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Linearly spaced sample points\n",
    "X=np.array(np.linspace(x_min,x_max,N_points))\n",
    "\n",
    "# Samples drawn from uniform random distribution\n",
    "X_sample = x_min+np.random.rand(N_points)*(x_max-x_min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def func(x):\n",
    "    result = (20*x+3*x**2+0.1*x**3)*np.sin(x)*np.exp(-(1/x_max)*x)\n",
    "    return (result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "noise_x = np.random.normal(loc=noise_mean,scale=noise_sd,size=N_points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "y = func(X)+noise_x\n",
    "y_sampled = func(X_sample)+noise_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Ideal y</th>\n",
       "      <th>y</th>\n",
       "      <th>X_sampled</th>\n",
       "      <th>y_sampled</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>17.588211</td>\n",
       "      <td>15.650784</td>\n",
       "      <td>3.183910</td>\n",
       "      <td>-4.931815</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.018036</td>\n",
       "      <td>18.122428</td>\n",
       "      <td>18.928283</td>\n",
       "      <td>1.616885</td>\n",
       "      <td>35.310703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.036072</td>\n",
       "      <td>18.658563</td>\n",
       "      <td>19.877147</td>\n",
       "      <td>5.834103</td>\n",
       "      <td>-56.593429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.054108</td>\n",
       "      <td>19.196234</td>\n",
       "      <td>20.407360</td>\n",
       "      <td>4.526172</td>\n",
       "      <td>-99.567634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.072144</td>\n",
       "      <td>19.735056</td>\n",
       "      <td>15.576878</td>\n",
       "      <td>8.827200</td>\n",
       "      <td>107.343905</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          X    Ideal y          y  X_sampled   y_sampled\n",
       "0  1.000000  17.588211  15.650784   3.183910   -4.931815\n",
       "1  1.018036  18.122428  18.928283   1.616885   35.310703\n",
       "2  1.036072  18.658563  19.877147   5.834103  -56.593429\n",
       "3  1.054108  19.196234  20.407360   4.526172  -99.567634\n",
       "4  1.072144  19.735056  15.576878   8.827200  107.343905"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(data=X,columns=['X'])\n",
    "df['Ideal y']=df['X'].apply(func)\n",
    "df['y']=y\n",
    "df['X_sampled']=X_sample\n",
    "df['y_sampled']=y_sampled\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plot the function(s), both the ideal characteristic and the observed output (with process and observation noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x208d4ed0e80>]"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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ChoY8YD7QAfv2/zrKwqUvBXAiIpJWJky4haqqfOAzbCzGQOAdVDqtmzU0bMN2ws7C5sP1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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d2dbbb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter('X','Ideal y',title='Ideal y',grid=True,edgecolors=(0,0,0),c='blue',s=40,figsize=(10,5))\n",
    "plt.plot(x_smooth,func(x_smooth),'k')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x208d33cffd0>]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8NPy234tXJ03xdMjVWuPGjckusBBzHRS7YNKnZruspVr5SBInhBDCo+x2O6FB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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d4ee56a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.plot.scatter('X_sampled',y='y_sampled',title='Randomly sampled y',\n",
    "                grid=True,edgecolors=(0,0,0),c='orange',s=40,figsize=(10,5))\n",
    "plt.plot(x_smooth,func(x_smooth),'k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import scikit-learn librares and prepare train/test splits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import LassoCV\n",
    "from sklearn.linear_model import RidgeCV\n",
    "from sklearn.ensemble import AdaBoostRegressor\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.pipeline import make_pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df['X'], df['y'], test_size=0.33)\n",
    "X_train=X_train.values.reshape(-1,1)\n",
    "X_test=X_test.values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_train=X_train.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Polynomial model with Ridge regularization (pipelined) with lineary spaced samples\n",
    "** This is an advanced machine learning method which prevents over-fitting by penalizing high-valued coefficients i.e. keep them bounded **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 2: 0.11788061639096882\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 3: 0.4880371335102572\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 4: 0.6690914027641579\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 5: 0.762422405048564\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 6: 0.8219635627413664\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 7: 0.8490620637574158\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 8: 0.8533903011616155\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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We6Cc9Wqr9tyhb0x7MRzXqfs5rinPVBbFjeR7AtfE/W/cyazFGqZfEtYsZowxpuAsczHG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\nRwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208cd160160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yXydkqda+kWIRJ3HlPFUdISIvqOohIlIPPKmqR5VGxM5hiSuNUpKqJNZ9sDl0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\nA2WR8lf6vRZxPDX37OSFqtonzw9wIDA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      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d64dd128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HXHr16qUDBgwotxiGYRgVxZw5c95X1aiSQlmpeuUyYMAAZs+uyEn5DMMwyoa4ubHyxtxi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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d65780f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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dA1/9anLjW29tLTQZp1hnn17hIxii2o3KJqNyUdVOVf2tqn5FVc/0PpeHHW8Y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\nO/8fSEsSZKuV2ecAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d661fba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MfS9r1jilcvXVXcufey40F1i6EOhCjNyM0iGOWexiYATwCYCq/h+wQz6FMoxK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\n7/Un37ZhIrJQRN4Ukd+KiIS3bhiGYRS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      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d66a46d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VqJRCWWn3yqVPnz7Mn1+Ri/IZhmGUDHFrY+WNmcUMwzCMxDHlYhiGYSSOKRfDMAwjcUy5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\nMh/2fjunAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d670eba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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aZLfd3Oj6IPPmQb/c9AQyHRSa7SBSo+N0tPxLnJjLZ97c9d8Bvi4iXYDqbA9o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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d6742828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "linear_sample_score = []\n",
    "poly_degree = []\n",
    "for degree in range(degree_min,degree_max+1):\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), RidgeCV(alphas=ridge_alpha,normalize=True,cv=5))\n",
    "    model = make_pipeline(PolynomialFeatures(degree), LassoCV(eps=lasso_eps,n_alphas=lasso_nalpha, \n",
    "                                                                  max_iter=lasso_iter,normalize=True,cv=5))\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), LinearRegression(normalize=True))\n",
    "    model.fit(X_train, y_train)\n",
    "    y_pred = np.array(model.predict(X_train))\n",
    "    test_pred = np.array(model.predict(X_test))\n",
    "    RMSE=np.sqrt(np.sum(np.square(y_pred-y_train)))\n",
    "    test_score = model.score(X_test,y_test)\n",
    "    linear_sample_score.append(test_score)\n",
    "    poly_degree.append(degree)\n",
    "    print(\"Test score of model with degree {}: {}\\n\".format(degree,test_score))\n",
    "    \n",
    "    #plt.figure()\n",
    "    #plt.title(\"RMSE: {}\".format(RMSE),fontsize=10)\n",
    "    #plt.suptitle(\"Polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    #plt.xlabel(\"X training values\")\n",
    "    #plt.ylabel(\"Fitted and training values\")\n",
    "    #plt.scatter(X_train,y_pred)\n",
    "    #plt.scatter(X_train,y_train)\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.title(\"Predicted vs. actual for polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    plt.xlabel(\"Actual values\")\n",
    "    plt.ylabel(\"Predicted values\")\n",
    "    plt.scatter(y_test,test_pred)\n",
    "    plt.plot(y_test,y_test,'r',lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.11788061639096882,\n",
       " 0.48803713351025718,\n",
       " 0.66909140276415791,\n",
       " 0.76242240504856396,\n",
       " 0.82196356274136639,\n",
       " 0.84906206375741577,\n",
       " 0.85339030116161552]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "linear_sample_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Modeling with randomly sampled data set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df['X_sampled'], df['y_sampled'], test_size=0.33)\n",
    "X_train=X_train.values.reshape(-1,1)\n",
    "X_test=X_test.values.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 2: 0.1646914433570139\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 3: 0.4733566651449164\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 4: 0.612138190592894\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 5: 0.709418049404799\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 6: 0.7821151062356136\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 7: 0.8223971506912691\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\coordinate_descent.py:491: ConvergenceWarning: Objective did not converge. You might want to increase the number of iterations. Fitting data with very small alpha may cause precision problems.\n",
      "  ConvergenceWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test score of model with degree 8: 0.8343946837221697\n",
      "\n"
     ]
    },
    {
     "data": {
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GcsK+w0s2p+WUM/DgtSXLSk65k7P4vR7OufVpRl/4h6ZsUitZc2kESR8CBpjZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d69a3208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Tl/R11eiKvDlwJHA8sDfBLY5vNLNHS91oqowFwaXDzN6MpF0MLDWzCyVNBAaa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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d6823748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ecOQYLn5gcd7yJvm27XMH/otfwLe/ndve4P9/p/eUfZyLpEEE5V9GE4xzAcDM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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d79e0eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8WxkMKuoay06RnnTPFZz45B9y6mUGQzZENptT9+SzXDaqmhSO0yQkLWqVSUlO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\nZ89HNJbSkgH7ww+Hu2MmW2j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3wLX9gsB9tCfwGnB5TYV1onzUzPYEDgVOlfTx6M7QKm7o\nMQXNcA34b6gPvsxxFmZ2cAmHdQPbRra3Ccu6w8/Z5TUh7bVJ+jVwV7iZdG2NQCPL3ouZdYf/35B0\nO4FL5XVJW5nZa6H79Y2aClkaSdfQkPfNzF7PfG6i31DJuOVSHu4ATpC0nqSRwA7A46HJ/46k/cIs\nsS8Bv6+loEmEP+4MRwOZLJjYa6u2fCXyBLCDpJGSBgEnEFxPwyBpA0kbZT4DnyK4N3cAJ4XVTqJO\nn6sCJF1DQz5zTfobKhm3XIpA0tHAT4DNgemS5pjZODObJ2kq8AywBjjVzNaGh30TmAJ0EGSL3VN9\nyVNxiaQ9CVwTi4CvAxS4trrGzNZIOg24jyBz7Gozm1djsYplS+D2MIN9IPA7M7tX0hPAVElfJVhS\n4rgaylgQSTcABwKbSVoMnAdMJuYaGuGZS7ieA5vtN9QffPoXx3Ecp+y4W8xxHMcpO65cHMdxnLLj\nysVxHMcpO65cHMdxnLLjysVxHMcpO65cnJZF0nhJJmmnFHVPlrR1P851oKS7CtesTjuOU2lcuTit\nzInAn8P/hTgZKFm5OE6r4crFaUkkbQh8FPgqwcj96L6zw/VT5kqaLOkzQBdwfbhOR0e4xspmYf0u\nSY+En/eR9FdJsyX9RdKoAnLMkDQ6sv1I2F7BdsL1Q74d2X5a0ojw8xckPR7K+ytJbeHflLDeU5LO\nLO3bc5zC+Ah9p1U5CrjXzJ6T9Kakvc1slqRDw337mtkKScPMbFk40v/bZpZZrCup3fnAx8LZAQ4G\n/gc4No8cNxGMTD8vnD5kKzObKWnjItvpRdLOwPHA/mbWI+nnwOeBeUCnme0a1huSpj3HKQVXLk6r\nciLw4/DzjeH2LOBg4BozWwFgZmnX7MiwCXCtpB0IpgFpL1B/KvAHgulDjgNuKbGdKJ8A9gaeCJVg\nB8GkkHcC20v6CTA9PK/jVARXLk7LIWkYcBCwmyQjmHfMJE0oopk1vO9WXj9S/n3gYTM7OnRRPZKv\nETPrDi2n3QmsjX8vop2oDFE5BFxrZudkHyBpD2BceJ7jgK/kk89xSsVjLk4r8hngN2a2nZmNMLNt\ngYXAx4D7gS9LGgy9igjgn8BGkTYWEVgH0NddtQnvT6d+ckp5bgL+C9jEzJ4sop1FBEvtImkvgiV0\nAR4EPiNpi8w1SNoujBENMLNbgXMzxzpOJXDl4rQiJwK3Z5XdCpxoZvcSTJE+U9IcIBMwnwL8MhPQ\nBy4AfixpJhCd4fYSYJKk2aT3DNxCkFQwtch2bgWGSZoHnAY8B2BmzxAojz9IepJAYW5FsPrhI+F1\n/RbIsWwcp1z4rMiO4zhO2XHLxXEcxyk7rlwcx3GcsuPKxXEcxyk7rlwcx3GcsuPKxXEcxyk7rlwc\nx3GcsuPKxXEcxyk7/z95T1fZlEM/EgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d7a45f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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2g3JaIF3dPcy4afmWbaOd9YX6NfrVGd7dDYMH5xRvaH8Nd97zSEFR8LBhpxAF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\nMIJQ5M+Z2XNVsK0pyDeALuN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      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d7acaf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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5GGFr1wbFXzGBZcI5s5n58LLu58XM5NjXTqOu8eXNuZjZWuCP4Z9zLlRIpXZS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\n/nzKwYNLabQBL0aeLwuXtYWPs5fXqv8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      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d7b42e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SMGpkO2+8vWxFXRO80+nRg8nwkKWH/hIzW5p7ImkVGFIRq3MtoZSirbTe9n39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\nLs455yrOg4tzzrmK+/9Yfe+Lg+iD5AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d7b5d6a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "random_sample_score = []\n",
    "poly_degree = []\n",
    "for degree in range(degree_min,degree_max+1):\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), RidgeCV(alphas=ridge_alpha,normalize=True,cv=5))\n",
    "    model = make_pipeline(PolynomialFeatures(degree), LassoCV(eps=lasso_eps,n_alphas=lasso_nalpha, \n",
    "                                                                  max_iter=lasso_iter,normalize=True,cv=5))\n",
    "    #model = make_pipeline(PolynomialFeatures(degree), LinearRegression(normalize=True))\n",
    "    model.fit(X_train, y_train)\n",
    "    y_pred = np.array(model.predict(X_train))\n",
    "    test_pred = np.array(model.predict(X_test))\n",
    "    RMSE=np.sqrt(np.sum(np.square(y_pred-y_train)))\n",
    "    test_score = model.score(X_test,y_test)\n",
    "    random_sample_score.append(test_score)\n",
    "    poly_degree.append(degree)\n",
    "    \n",
    "    print(\"Test score of model with degree {}: {}\\n\".format(degree,test_score))\n",
    "    \n",
    "    #plt.figure()\n",
    "    #plt.title(\"RMSE: {}\".format(RMSE),fontsize=10)\n",
    "    #plt.suptitle(\"Polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    #plt.xlabel(\"X training values\")\n",
    "    #plt.ylabel(\"Fitted and training values\")\n",
    "    #plt.scatter(X_train,y_pred)\n",
    "    #plt.scatter(X_train,y_train)\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.title(\"Predicted vs. actual for polynomial of degree {}\".format(degree),fontsize=15)\n",
    "    plt.xlabel(\"Actual values\")\n",
    "    plt.ylabel(\"Predicted values\")\n",
    "    plt.scatter(y_test,test_pred)\n",
    "    plt.plot(y_test,y_test,'r',lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.16469144335701391,\n",
       " 0.47335666514491642,\n",
       " 0.61213819059289398,\n",
       " 0.70941804940479902,\n",
       " 0.78211510623561364,\n",
       " 0.82239715069126906,\n",
       " 0.83439468372216974]"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random_sample_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Linear sample score</th>\n",
       "      <th>Random sample score</th>\n",
       "      <th>degree</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.117881</td>\n",
       "      <td>0.164691</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.488037</td>\n",
       "      <td>0.473357</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.669091</td>\n",
       "      <td>0.612138</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.762422</td>\n",
       "      <td>0.709418</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.821964</td>\n",
       "      <td>0.782115</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.849062</td>\n",
       "      <td>0.822397</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.853390</td>\n",
       "      <td>0.834395</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Linear sample score  Random sample score  degree\n",
       "0             0.117881             0.164691       2\n",
       "1             0.488037             0.473357       3\n",
       "2             0.669091             0.612138       4\n",
       "3             0.762422             0.709418       5\n",
       "4             0.821964             0.782115       6\n",
       "5             0.849062             0.822397       7\n",
       "6             0.853390             0.834395       8"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_score = pd.DataFrame(data={'degree':[d for d in range(degree_min,degree_max+1)],\n",
    "                              'Linear sample score':linear_sample_score,\n",
    "                              'Random sample score':random_sample_score})\n",
    "df_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x208d7e30f98>"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Qk+C7nWUryRlj6gW3q9cdB3wDNAWW4BTIOThUeBjwG+BqP8RnzBHLOFDAtZMX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\nMdbQWywWi8VSjLGG3mKxWCyWYsz/A3luL0B4g2/jAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d4ee55c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,5))\n",
    "plt.grid(True)\n",
    "plt.plot(df_score['degree'],df_score['Linear sample score'],lw=2)\n",
    "plt.plot(df_score['degree'],df_score['Random sample score'],lw=2)\n",
    "plt.xlabel (\"Model Complexity: Degree of polynomial\",fontsize=20)\n",
    "plt.ylabel (\"Model Score: R^2 score on test set\",fontsize=15)\n",
    "plt.legend(fontsize=15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cehcking the regularization strength from the cross-validated model pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0014941809717564625"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m=model.steps[1][1]\n",
    "m.alpha_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural network for regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Import and declaration of variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "learning_rate = 0.000001\n",
    "training_epochs = 20000\n",
    "\n",
    "n_input = 1  # Number of features\n",
    "n_output = 1  # Regression output is a number only\n",
    "\n",
    "n_hidden_layer = 35 # layer number of features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:3: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:4: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "  after removing the cwd from sys.path.\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:5: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "  \"\"\"\n",
      "C:\\Users\\Tirtha\\Python\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:6: FutureWarning: reshape is deprecated and will raise in a subsequent release. Please use .values.reshape(...) instead\n",
      "  \n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(df['X'], df['y'], test_size=0.33)\n",
    "\n",
    "X_train=X_train.reshape(X_train.size,1)\n",
    "y_train=y_train.reshape(y_train.size,1)\n",
    "X_test=X_test.reshape(X_test.size,1)\n",
    "y_test=y_test.reshape(y_test.size,1)\n",
    "\n",
    "from sklearn import preprocessing\n",
    "X_scaled = preprocessing.scale(X_train)\n",
    "y_scaled = preprocessing.scale(y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Weights and bias variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Store layers weight & bias as Variables classes in dictionaries\n",
    "weights = {\n",
    "    'hidden_layer': tf.Variable(tf.random_normal([n_input, n_hidden_layer])),\n",
    "    'out': tf.Variable(tf.random_normal([n_hidden_layer, n_output]))\n",
    "}\n",
    "biases = {\n",
    "    'hidden_layer': tf.Variable(tf.random_normal([n_hidden_layer])),\n",
    "    'out': tf.Variable(tf.random_normal([n_output]))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of the weights tensor of hidden layer: (1, 35)\n",
      "Shape of the weights tensor of output layer: (35, 1)\n",
      "--------------------------------------------------------\n",
      "Shape of the bias tensor of hidden layer: (35,)\n",
      "Shape of the bias tensor of output layer: (1,)\n"
     ]
    }
   ],
   "source": [
    "print(\"Shape of the weights tensor of hidden layer:\",weights['hidden_layer'].shape)\n",
    "print(\"Shape of the weights tensor of output layer:\",weights['out'].shape)\n",
    "print(\"--------------------------------------------------------\")\n",
    "print(\"Shape of the bias tensor of hidden layer:\",biases['hidden_layer'].shape)\n",
    "print(\"Shape of the bias tensor of output layer:\",biases['out'].shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Weight tensor initialized randomly\n",
      "---------------------------------------\n",
      " [[ 1.04348898 -0.62562287  0.0830955  -0.2694059  -1.59905183  1.82611179\n",
      "  -0.21245536 -1.21637654  0.97147286 -0.08349181 -1.6938988   0.7615844\n",
      "   1.4193033   1.52271056 -0.26382461 -0.66391391  0.62335193 -0.64882958\n",
      "   0.34043887  0.51017839 -1.31694865 -0.38064736  1.18706989  0.3256394\n",
      "  -1.07438827  0.99597555 -0.84235168 -0.14966556 -0.07332329  0.45747992\n",
      "  -0.90638632  0.38841721 -1.22614443 -1.21204579 -2.03451443]]\n",
      "Bias tensor initialized randomly\n",
      "---------------------------------------\n",
      " [ 0.42340374  0.19241172 -0.32600278  0.70526534  0.61445254  0.15266864\n",
      "  0.51332366  1.05123603  0.49825382  0.58842802  1.42681241  0.90139294\n",
      "  0.25430983  0.70529252 -0.16479528  1.69503176  0.94038701  0.32357663\n",
      "  0.61296964 -0.77653986  0.07061771  1.3192941   0.12997486  0.4277775\n",
      "  0.37885833  1.02218032  0.81157911  0.29033285  0.521981    0.20968065\n",
      " -0.46419618  0.01151479 -0.11108538 -0.60381615  0.17639446]\n"
     ]
    }
   ],
   "source": [
    "with tf.Session() as sess:\n",
    "    sess.run(tf.global_variables_initializer())\n",
    "    w=sess.run(weights['hidden_layer'])\n",
    "    b=sess.run(biases['hidden_layer'])\n",
    "print(\"Weight tensor initialized randomly\\n---------------------------------------\\n\",w)\n",
    "print(\"Bias tensor initialized randomly\\n---------------------------------------\\n\",b)\n",
    "sess.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Input data as placeholder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# tf Graph input\n",
    "x = tf.placeholder(\"float32\", [None,n_input])\n",
    "y = tf.placeholder(\"float32\", [None,n_output])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hidden and output layers definition (using TensorFlow mathematical functions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Hidden layer with RELU activation\n",
    "layer_1 = tf.add(tf.matmul(x, weights['hidden_layer']),biases['hidden_layer'])\n",
    "layer_1 = tf.nn.relu(layer_1)\n",
    "\n",
    "# Output layer with linear activation\n",
    "ops = tf.add(tf.matmul(layer_1, weights['out']), biases['out'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gradient descent optimizer for training (backpropagation):\n",
    "For the training of the neural network we need to perform __backpropagation__ i.e. propagate the errors, calculated by this cost function, backwards through the layers all the way up to the input weights and bias in order to adjust them accordingly (minimize the error). This involves taking first-order derivatives of the activation functions and applying chain-rule to ___'multiply'___ the effect of various layers as the error propagates back.\n",
    "\n",
    "You can read more on this here: [Backpropagation in Neural Network](https://en.wikipedia.org/wiki/Backpropagation)\n",
    "\n",
    "Fortunately, TensorFlow already implicitly implements this step i.e. takes care of all the chained differentiations for us. All we need to do is to specify an Optimizer object and pass on the cost function. Here, we are using a Gradient Descent Optimizer.\n",
    "\n",
    "Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient (or of the approximate gradient) of the function at the current point.\n",
    "\n",
    "You can read more on this: [Gradient Descent](https://en.wikipedia.org/wiki/Gradient_descent)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Define loss and optimizer\n",
    "cost = tf.reduce_sum(tf.squared_difference(ops,y))\n",
    "optimizer = tf.train.GradientDescentOptimizer(learning_rate=learning_rate).minimize(cost)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### TensorFlow Session for training and loss estimation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████████████████████████████████████████| 20000/20000 [00:21<00:00, 942.58it/s]\n"
     ]
    }
   ],
   "source": [
    "from tqdm import tqdm\n",
    "\n",
    "# Initializing the variables\n",
    "init = tf.global_variables_initializer()\n",
    "\n",
    "# Empty lists for book-keeping purpose\n",
    "epoch=0\n",
    "log_epoch = []\n",
    "epoch_count=[]\n",
    "acc=[]\n",
    "loss_epoch=[]\n",
    "\n",
    "# Launch the graph\n",
    "with tf.Session() as sess:\n",
    "    sess.run(init)    \n",
    "    # Loop over epochs\n",
    "    for epoch in tqdm(range(training_epochs)):\n",
    "        # Run optimization process (backprop) and cost function (to get loss value)\n",
    "        _,l=sess.run([optimizer,cost], feed_dict={x: X_scaled, y: y_scaled})\n",
    "        loss_epoch.append(l) # Save the loss for every epoch        \n",
    "        epoch_count.append(epoch+1) #Save the epoch count\n",
    "       \n",
    "        # print(\"Epoch {}/{} finished. Loss: {}, Accuracy: {}\".format(epoch+1,training_epochs,round(l,4),round(accu,4)))\n",
    "        #print(\"Epoch {}/{} finished. Loss: {}\".format(epoch+1,training_epochs,round(l,4)))\n",
    "    w=sess.run(weights)\n",
    "    b = sess.run(biases)\n",
    "    #layer_1 = tf.add(tf.matmul(X_test, w['hidden_layer']),b['hidden_layer'])\n",
    "    #layer_1 = tf.nn.relu(layer_1)\n",
    "\n",
    "    # Output layer with no activation\n",
    "    #ops = tf.add(tf.matmul(layer_1, w['out']), b['out'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "layer1=np.matmul(X_test,w['hidden_layer'])+b['hidden_layer']\n",
    "layer1_out = np.maximum(layer1,0)\n",
    "yhat = np.matmul(layer1_out,w['out'])+b['out']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat-y_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x208d7c5f5f8>]"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DrsTMbPnJPgQ+uGE1V69fxe88/QYR3iVkZlaWfQhI4p/+9Wt55s9/xH9+7M8cBGZmJdmH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\nmdkI+/9VA8wPBLyGhwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d1444cf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(epoch_count,loss_epoch)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(335, 1)"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_scaled.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_46 (Dense)             (None, 25)                50        \n",
      "_________________________________________________________________\n",
      "dense_47 (Dense)             (None, 25)                650       \n",
      "_________________________________________________________________\n",
      "dense_48 (Dense)             (None, 25)                650       \n",
      "_________________________________________________________________\n",
      "dense_49 (Dense)             (None, 25)                650       \n",
      "_________________________________________________________________\n",
      "dense_50 (Dense)             (None, 1)                 26        \n",
      "=================================================================\n",
      "Total params: 2,026\n",
      "Trainable params: 2,026\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Imports\n",
    "import numpy as np\n",
    "from keras.models import Sequential\n",
    "from keras.layers.core import Dense, Dropout, Activation\n",
    "from keras.optimizers import SGD\n",
    "from keras.utils import np_utils\n",
    "\n",
    "# Building the model\n",
    "model = Sequential()\n",
    "model.add(Dense(25, activation='linear', input_dim=1))\n",
    "#model.add(Dropout(.2))\n",
    "model.add(Dense(25, activation='linear'))\n",
    "#model.add(Dropout(.1))\n",
    "model.add(Dense(25, activation='linear'))\n",
    "model.add(Dense(25, activation='linear'))\n",
    "model.add(Dense(1, activation='linear'))\n",
    "\n",
    "# Compiling the model\n",
    "sgd = SGD(lr=0.001, decay=0, momentum=0.9, nesterov=True)\n",
    "model.compile(loss = 'mean_squared_error', optimizer='sgd')\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x208d7bb7da0>"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_scaled, y_scaled, epochs=2000, verbose=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "165/165 [==============================] - ETA:  - 0s 608us/step\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "8059.3590613162878"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "score = model.evaluate(X_test, y_test)\n",
    "score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "yhat=model.predict(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "yhat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x208d67c04a8>"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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iFZnuNAMBGYmL25ARvLIvnG0bR55c9e8QsNOYzMWaASXCatNABcC9W3tYKyBj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\nEYHBgIiIwGBARERgMCAiIjAYEBERgP8H5p2yv+QEbaUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x208d7bb7d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(yhat,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
